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Undergraduate Algebra is a text for the standard undergraduate algebra course. It concentrates on the basic structures and results of algebra, discussing groups, rings, modules, fields, polynomials, finite fields, Galois Theory, and other topics. The author has also included a chapter on groups of matrices which is unique in a book at this level. Throughout the book, the author strikes a balance between abstraction and concrete results, which enhance each other. Illustrative examples accompany the general theory. Numerous exercises range from the computational to the theoretical, complementing results from the main text.
For the third edition, the author has included new material on product structure for matrices (e.g. the Iwasawa and polar decompositions), as well as a description of the conjugation representation of the diagonal group. He has also added material on polynomials, culminating in Noah Snydera (TM)s proof of the MasonStothers polynomial abc theorem.
About the First Edition:
The exposition is downtoearth and at the same time very smooth. The book can be covered easily in a oneyear course and can be also used in a oneterm course...the flavor of modern mathematics is sprinkled here and there.
 Hideyuki Matsumura, Zentralblatt